it looks to me like your psd file has some transparent areas that are not fully transparent - have you checked that there is no redundant pixels in the trans area? I would also make a selection of your trans area (in ps), expand it one or two px and delete - see if that has any efect on your ai file.
Alternatively you could mask the object in ai. I have done this: copy the image auto trace so that you get only an outline of the bit you want - ignore white - expand and paste the image behind - select all and make clipping mask. you can then adjust the mask to get a perfect fit.
I think in this case it might be better to simply mask it in AI as it
does seem not to be a clean silhouette as you can easily see other
I think a clean path in AI will give you the hard edge clean
silhouette you are looking for.
This is a pdf made from Illustrator with the clipping mask also mad in Illustrator.
Of course if I had the original and not a screenshot things would look much better
But you get the idea, You could go back to Photoshop an do some more careful erasing of the background.
Here is the path I used to make the clipping it takes about 5-10 minutes
And if you want a drop shadow that might be best in Illy as well
some of the other guys like Scott and James and Hans could d this better but the level of skill and practice is always importat.
Now if you want it a little softer on the edges I would then go back to Photoshop do a more detailed silhouette and give it a light feather in Photoshop.